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Introduction to Discrete Mathematics, by Robert J. McEliece, Robert B. Ash, Carol Ash
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As a complete introduction to all of the important areas in discrete mathematics - and as preparation for advanced courses in computer science or electrical engineering with discrete mathematics as a prerequisite - this text is ideal. The authors are well-known, highly respected mathematicians with many years of practical experience. They have included all parts of the subject that are essential for all practical applications, plus some less directly applicable topics which are intellectually challenging and fun (combinatorics, Euler's V-E+F=2 theorem, and mathematical games). More than 200 worked examples, 1,500 problems, and 600 figures are included.
- Sales Rank: #2146517 in Books
- Published on: 1989-06
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 477 pages
Most helpful customer reviews
5 of 5 people found the following review helpful.
An excellent textbook on discrete mathematics
By Jill Malter
As the authors explain, discrete mathematics is supposed to be mathematics that uses only arithmetic and algebra but does not involve calculus. That gives the authors plenty of flexibility in choosing their topics. And I'll concede that the material on "propositional calculus" in Chapter Five does not involve "calculus." You can understand this book without having gone past high school algebra.
These authors have the right idea when they say "an undergraduate mathematics textbook should teach the student to solve problems." This text sure does! And they even advise their students to start by trying the homework problems before reading the text and read it only when they get stuck! Of course, I think many students do that in the first place.
A very good feature of this text is that it has over 600 figures and tables. We see Venn diagrams, Hasse diagrams, tree diagrams, graphs, flowcharts, state diagrams, and much more.
I liked the part on graph theory, including the "Hungarian Algorithm" to solve the matching problem. And there is a good chapter on Boolean Algebra, and the use of Karnaugh maps. After that is an excellent section on finite state machines and Turing machines, which is followed by a chapter on formal languages. And there's plenty about mathemtical games. The whole book is enjoyable, and I think it would be plenty of fun to teach from it or learn from it.
4 of 5 people found the following review helpful.
Exhausting textbook.
By Benjamin L. Russell
I used this book for the course "Computer Science 202a: Mathematical Tools for Computer Science," at Yale University in the fall semester of 1991 - 92, which I audited. This was a required course in mathematical foundations for the computer science major.
I didn't like this book. While extremely thorough, it goes to an extreme. Some of the exercises, especially in the chapter on Discrete Probability Theory, were extremely long-winded, and took many hours and pages to solve. My writing hand eventually got tired from writing page after page after page for some of the exercises, and I once wound up with a severe headache during that course. While this textbook definitely teaches the student to "solve problems," it does so by exhausting the student.
The problem with the book's approach of urging students to "start by trying the homework problems before reading the text, and read it only when they get stuck" is that this approach does not help to build self-confidence for students who do not already have a flair for this material, yet the textbook is used in introductory courses for non-mathematics (e.g., computer science) majors. At this level, many students who many be proficient in other topics (e.g., programming) may just be getting their feet wet in this material.
It does not make sense to use this approach to help build self-confidence in an introductory discrete mathematics course for non-mathematics majors. My professor once conducted an in-class poll of how much time the students were spending on each weekly homework assignment using this textbook, and the average was about twenty hours. (This finding caused the professor to revise the homework policy from long problem sets to weekly examinations [which was even worse for students with examination phobia].)
My view is that many of the problems could have been designed to take less time each, while preserving the required ingenuity. There were simply too many steps required to complete many of the problems. In my opinion, this aspect was especially true of the chapter on Discrete Probability Theory.
The chapter on Graph Theory was fun, though, and the Venn diagrams were lucid. Also, the chapter on Propositional Calculus was relatively reasonable in difficulty, as well as being interesting. The chapters on Number Theory and Mathematical Games were interesting as well.
In particular, I felt that the chapter on Mathematical Games, which was independent of the other chapters, should have been placed earlier. That chapter, unlike some of the others, was relatively light and interesting, and would have helped to build self-confidence for students before they tackled some of the more serious material.
In sum, this textbook has a "tackle first, read later" approach toward learning, which is not always conducive toward building self-confidence: Its approach is like teaching one to swim by throwing one into a pool and seeing how close one gets to drowning before lending a minimalist hand. If you read it, you'll definitely learn how to solve problems extremely well, but you may not preserve your sanity. It is like taking a drink from a fire hydrant.
Benjamin L. Russell
0 of 0 people found the following review helpful.
Excellent for self learners. Better than contemporary texts. Nice applications
By vegas physics
This is an excellent textbook for self learners or anyone else who wants to learn the subject. The prerequisites are low, only high school algebra, but the coverage is thorough. The answers to the odd numbered problems are fairly detailed, many are outline solutions rather than just final answers. It is not as theoretical as Rosen, but has lots of nice applications. The authors philosophy is learning by doing. If you are willing to work lots of problems in this text, you will be just as well prepared as some one who studyied from a more advanced book.
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